Consider nonlinear circuit system displayed in Figure 4, where a dc source with voltage [mu] is connected in series to a linear resistor, a linear inductor, and a nonlinear capacitor
with a q-v characteristic q = z(v) = (v - [v.sub.0]) + [(v - [v.sub.0]).sup.3] + [q.sub.0].
Its capacitance is assumed to be expanded as a power series of the local signal voltage [V.sub.n], which appears across the nonlinear capacitor of the nth cell:
where [C.sub.0] [equivalent to] C([V.sub.b]) is a constant corresponding to the capacitance of the nonlinear capacitor at the dc bias voltage [V.sub.b], and [alpha] [equivalent to] C'([V.sub.b])/2C([V.sub.b]) is a parameter characterizing the nonlinearity while qn is the electrical charge stored in the nth capacitor.
If the NLR is replaced by a nonlinear capacitor, it is then possible to obtain modulated gray and dark compactons .
Increasing the doping density can be reflected in the model parameter [N.sub.D], which affects the device currents through Equation 1, and also affects the corresponding expressions for the nonlinear capacitor constitutive relations [Q.sub.b].
Nonlinear capacitors are defined by the functions [Q.sub.b.].
Each cell consists of a linear inductive element of inductance l and a linear resistor with resistance r1 in the series branch, which constitute the linear dispersive element, and a nonlinear capacitor
of capacitance c and a linear resistor with resistance r2 in the shunt branch.
A nonlinear capacitor
has an analogous relationship.
One of the key points in evaluating the nonlinearities in the modelling of power MOSFETs is to understand that the model is merely an equivalent circuit, and nonlinear capacitors
in the model are not physical capacitances , , although the model may resemble the physical structures.
In the proposition below, the result presented above is extended in the sense that the asymptotic stability properties are still guaranteed considering nonlinear capacitors
Hakkak, "Bright and dark soliton generation in a left-handed nonlinear transmission line with series nonlinear capacitors
," Progress In Electromagnetics Research, Vol.
The nonlinear capacitors
present in the MESFET are modeled by the Schottky barrier diode junction capacitance as a function of junction voltage.